SOLUTION: Worker A can finish the job in 5 hrs, Worker B in 6 hrs. If they split the work in half and worker A starts the work, how long will it take to finish the job? I tried work rate

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Question 1196982: Worker A can finish the job in 5 hrs, Worker B in 6 hrs.
If they split the work in half and worker A starts the work, how long will it take to finish the job?
I tried work rate approach:
X(1/5+1/6)=1
X=30/11=2.7 hrs but this seem too short
Found 3 solutions by ikleyn, josgarithmetic, greenestamps:
Answer by ikleyn(52884)   (Show Source): You can put this solution on YOUR website!
.
Worker A can finish the job in 5 hrs, Worker B in 6 hrs.
If they split the work in half and worker A starts the work, how long will it take to finish the job?
~~~~~~~~~~~~~~~~~~ 

The problem says that they split the work in half.


As I understand these words, it means that A makes one half of the job, and B makes the remaining half.


Then A will complete his half in 5/2 = 2.5 hours;  B will complete his half of the job in 6/2 = 3 hours.


    If B works after A (in this case they DO NOT work simultaneously), 
    then the gob will be complete in 2.5 + 3 hours = 5.5 hours.


    If, in opposite,  they start simultaneously, then the entire job will be 
    complete when B will complete his part, i.e. in 3 hours.

Solved.

As I interpret this problem, it is NOT classic joint work problem - - - they are worded differently.

It is different kind of problems.



Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
Splitting the work in half
         workrate      Time                 amount of work

A          1/5        (1/2)/(1/5)=5/2          1/2

B          1/6        (1/2)/(1/6)=6/2=3        1/2

Worker A spent 2.5 hours, and worker B spent 3 hours.




Answer by greenestamps(13209)   (Show Source): You can put this solution on YOUR website!


The problem is worded very poorly, leaving it open to many different interpretations.

We know that A starts the work and does half of it, taking 2.5 hours; and we know B does the other half of the work, taking 3 hours.

But there is nothing that tells us when B starts the work.

If B starts right when A finishes, then of course it takes 2.5+3 = 5.5 hours to finish the job.

But if B starts working while A is still working, then the job will be finished in less than 5.5 hours.

And, the way the problem is worded, B might start his half of the job a day or a week after A finishes his half; in that case it takes far more than 5.5 hours to finish the job.

And yet another interpretation is that "how long will it take to finish the job" only means how long does it take B to finish the job after A does his half; the answer in that case is 3 hours.
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